@article{RSW04,
  title={The cyclic sieving phenomenon},
  author={Reiner, Victor and Stanton, Dennis and White, Dennis},
  journal={Journal of Combinatorial Theory, Series A},
  volume={108},
  number={1},
  pages={17--50},
  year={2004},
  publisher={Academic Press}
}

@unpublished{OS19,
  title={On cyclic quiver parabolic Kostka-Shoji polynomials},
  author={Orr, Daniel and Shimozono, Mark},
  eprint={1906.06758},
  eprinttype={arXiv},
  year={2019}
}

@article{LLT,
  title={Green polynomials and Hall-Littlewood functions at roots of unity},
  author={Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
  journal={European Journal of Combinatorics},
  volume={15},
  number={2},
  pages={173--180},
  year={1994},
  publisher={London: Academic Press, c1980-}
}

@article{Tanisaki,
  title={Defining ideals of the closures of the conjugacy classes and representations of the Weyl groups},
  author={Tanisaki, Toshiyuki},
  journal={Tohoku Mathematical Journal, Second Series},
  volume={34},
  number={4},
  pages={575--585},
  year={1982},
  publisher={Mathematical Institute, Tohoku University}
}

@article{Chevalley,
  title={Invariants of finite groups generated by reflections},
  author={Chevalley, Claude},
  journal={American Journal of Mathematics},
  volume={77},
  number={4},
  pages={778--782},
  year={1955},
  publisher={JSTOR}
}
@article{DP81,
  title={Symmetric functions, conjugacy classes and the flag variety},
  author={De Concini, Corrado and Procesi, Claudio},
  journal={Inventiones mathematicae},
  volume={64},
  number={2},
  pages={203--219},
  year={1981},
  publisher={Springer}
}

@article{BRS08,
  title={Bimahonian distributions},
  author={Barcelo, H{\'e}lene and Reiner, Victor and Stanton, Dennis},
  journal={Journal of the London Mathematical Society},
  volume={77},
  number={3},
  pages={627--646},
  year={2008},
  publisher={Oxford University Press}
}

@unpublished{OR20,
  title={Cyclic sieving and orbit harmonics},
  author={Oh, Jaeseong and Rhoades, Brendon},
  volume={},
  number={},
  pages={},
  eprint={2010.08074},
  eprinttype={arXiv},
  year={2020},
  publisher={}
}

@misc{GH08,
  title={Orbit harmonics and graded representations},
  author={Garsia, A. and Haiman, Mark}
}

@article{HHL04,
  title={A combinatorial formula for {M}acdonald polynomials},
  author={Haglund, Jim and Haiman, Mark and Loehr, Nick},
  journal={Journal of the American Mathematical Society},
  volume={18},
  number={3},
  pages={735--761},
  year={2005}
}

@unpublished{Rei18,
  title={Finite refelction groups and general linear groups},
  author={Reiner, Victor},
  journal={},
  volume={},
  number={},
  pages={},
  note={A Pan-Hemispheric Celebration of Math in Miami},
  year={2018},
  publisher={}
}


@unpublished{Oh20+,
  title={Macdonald polynomials and cyclic sieving},
  author={Oh, Jaeseong},
  volume={},
  number={},
  pages={},
  eprint={2102.09982},
  eprinttype={arXiv},
  year={2021},
  publisher={}
}


@article{Dou18,
  title={Cyclic sieving for reduced reflection factorizations 
of the Coxeter element},
  author={Douvropoulos, Theo},
  journal={\em S\'em. Loth. Combin.},
  volume={08B},
  pages={},
  year={2018},
  publisher={Elsevier}
}

@article{Kos63,
  title={Lie group representations on polynomial rings},
  author={Kostant, Bertram},
  journal={American Journal of Mathematics},
  volume={85},
  number={3},
  pages={327--404},
  year={1963},
  publisher={JSTOR}
}

@article{ARR15,
  title={Parking spaces},
  author={Armstrong, Drew and Reiner, Victor and Rhoades, Brendon},
  journal={Advances in Mathematics},
  volume={269},
  pages={647--706},
  year={2015},
  publisher={Elsevier}
}
@unpublished{HJO20+,
  title={cyclic sieving for twisted rotation},
  author={Oh, Jaeseong},
  note={in preparation},
  volume={},
  number={},
  pages={},
  publisher={}
}


@article{HRS18,
  title={Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture},
  author={Haglund, James and Rhoades, Brendon and Shimozono, Mark},
  journal={Advances in Mathematics},
  volume={329},
  pages={851--915},
  year={2018},
  publisher={Elsevier}
}

@article{GP92,
  title={On certain graded $\mathfrak{S}_n$-modules and the $q$-Kostka polynomials},
  author={Garsia, Adriano M and Procesi, Claudio},
  journal={Advances in Mathematics},
  volume={94},
  number={1},
  pages={82--138},
  year={1992},
  publisher={Elsevier}
}

@article{Spr74,
  title={Regular elements of finite reflection groups},
  author={Springer, Tonny Albert},
  journal={Inventiones mathematicae},
  volume={25},
  number={2},
  pages={159--198},
  year={1974},
  publisher={Springer}
}

@article{MN06,
  title={A formula of {L}ascoux-{L}eclerc-{T}hibon and representations of symmetric groups},
  author={Morita, Hideaki and Nakajima, Tatsuhiro},
  journal={Journal of Algebraic Combinatorics},
  volume={24},
  number={1},
  pages={45--60},
  year={2006},
  publisher={Springer}
}

@article{GH93,
  title={A graded representation model for Macdonald's polynomials.},
  author={Garsia, Adriano M and Haiman, Mark},
  journal={Proceedings of the National Academy of Sciences},
  volume={90},
  number={8},
  pages={3607--3610},
  year={1993},
  publisher={National Acad Sciences}
}

@article{Hai01,
  title={Hilbert schemes, polygraphs and the Macdonald positivity conjecture},
  author={Haiman, Mark},
  journal={Journal of the American Mathematical Society},
  volume={14},
  number={4},
  pages={941--1006},
  year={2001}
}

@article{AU19,
  title={Cyclic sieving, skew Macdonald polynomials and Schur positivity},
  author={Alexandersson, Per and Uhlin, Joakim},
  eprint={1908.00083},
  eprinttype={arXiv},
  year={2019}
}
@article{Hai99,
  title={Macdonald polynomials and geometry},
  author={Haiman, Mark},
  journal={New perspectives in algebraic combinatorics (Berkeley, CA, 1996--97)},
  volume={38},
  pages={207--254},
  year={1999}
}

@inproceedings{GH96,
  title={Some Natural Bigraded $\mathfrak{S}_n$-Modules and $q, t$-Kostka Coefficients.},
  author={Garsia, Adriano M and Haiman, Mark},
  booktitle={Electronic journal of combinatorics},
  year={1996},
}

@article{DM08,
  title={Factorization formulas for Macdonald polynomials},
  author={Descouens, Fran{\c{c}}ois and Morita, Hideaki},
  journal={European Journal of Combinatorics},
  volume={29},
  number={2},
  pages={395--410},
  year={2008},
  publisher={Elsevier}
}

@article{Rho10,
  title={Hall--Littlewood polynomials and fixed point enumeration},
  author={Rhoades, Brendon},
  journal={Discrete mathematics},
  volume={310},
  number={4},
  pages={869--876},
  year={2010},
  publisher={Elsevier}
}